First off, I love the phrase "made up history class thing".
I think it sort of depends on how one is choosing to interpret the concept, and it also changes quite a bit throughout its three thousand odd year history. If you take it to mean that the political leadership of China was constantly worried about whether it had the Mandate and whether it was an active topic of discussion in the court, no. There is a really great kind of poppy history book called 1587 that takes a handful of significant political actors and weaves the story of the Late Ming court. There is plenty to criticize (thr portrayal of the Ming military situation is abysmal) but it does a really good job of showing them motivated by rational, real world concerns and producing rational, real world decisions based on them, and if you are looking for a book that gives a good flavor of court discussion I would recommend it.
So in the sort of totalizing sense that it is sometimes presented as, I would say no, but there are a few ways in which it is still a valuable, primarily as a mode of historical explanation--one of the early acts of every dynasty was to commission a history of the previous dynasty, and the sort of unspoken purpose of this was to make it clear that the previous dynasty had lost of the favor of Heaven and the current dynasty thus ruled legitimately. But even here it is not total. In the early Song, for example, a group of well known scholars produced a revision of the official history called the New History of the Tang, which does not talk a lot about things like divine portents but speak a lot about trade and bureaucracy. Spatially, temporally, and demographically there is an awful lot of China which tends to crack any sort of generalization.
But I think there is another way to think about this, namely through the ideas behind the Mandate of Heaven. The earliest formulation of it we possess is from the Classic of History, in which the Duke of Zhou claimed that the Shang dynasty's immorality had lost them the favor of tien (conventionally translated as "heaven") and that the Zhou's usurpation of the Shang thus had divine sanction. I'm having a bizarrely difficult time finding the passage, but here is one translation. What is important to note here is that the concept of rulership is fundamentally meritocratic--the king's rule is not sanctioned based on his bloodline, or because he is fundamentally separate from the people, or because he is divine (the idea of the "Son of Heaven" is a tricky one that is too often mapped onto the idea of divine kingship, which misses the nuance). His rule is correct because he rules well, in line with moral virtue and his own duties. This was expanded enormously by Confucius and particularly Mencius, who say outright that a king's right to rule is fundamentally based on their own actions. A king who does not behave properly does not deserve the fealty of his subordinates.
Now we shouldn't get carried away here, but meritocracy has a very strong streak in the long history of Chinese civilization. This is most famously shown in the examination system, in which officials were chosen (in theory and often in practice) not for their personal connections or social status but for their merit and talents, shown through scholarly examination. It is also something that comes through often in didactic history--in Sima Qian's account of the rise of the Han Dynasty, the point is made repeatedly that Liu Bang triumphed over Xiang Yu, a far more capable military leader, because he promoted his subordinates based on merit and judged their ideas well and fairly.
So long story short, if you want to take the idea of the "Mandate of Heaven" as being a totalizing concept that everybody was super concerned about all the time, no, they generally worried about tax assessments and agricultural production. But if you take it to mean a fundamentally meritocratic view of rule, I would say yes.
Follow up question: Does or did the Communist Party of China claim to have the Mandate in any way, or is their justification to rule sort of an adaptation of the original Mandate?